more fuel burn due to higher numbers of squished bugs on the airframe?
There is no higher fuel burn. Let me remind you that fuel burn is a rate.
No, the TAS wil be lower and it will take more time to reach your destination. You will just take more time/pay more to reach the same destination.
There is certainly a financial aspect to it but I don't think it's that significant.
How many hours do you solo in the pattern? 5 to 10?
Imagining that half of that time is spent taxiing, you have 2.5 to 5 hours where the engine is turning at close to idle, saving maybe 4 gal/hour on a C-150 and around 6 gal/hour on a C-172/PA28.
That may save the school up to 100$ per student.
It is not really significant.
Don't forget that maintenance is a big cost for a school, certainly engine maintenance (about 20 000$ every 2000 hours).